WinForms Hiding TabControl Headers

You can use a Style applied to TabItem with a DataTrigger that will collapse it if the parent TabControl has only one item:

<Grid xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
      xmlns:sys="clr-namespace:System;assembly=mscorlib"
      xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml">
    <Grid.Resources>
        <x:Array x:Key="tabData" Type="{x:Type sys:String}">
            <sys:String>do</sys:String>
            <sys:String>re</sys:String>
            <sys:String>mi</sys:String>
        </x:Array>
    </Grid.Resources>
    <TabControl ItemsSource="{StaticResource tabData}">
        <TabControl.ItemContainerStyle>
            <Style TargetType="{x:Type TabItem}">
                <Style.Triggers>
                    <DataTrigger Binding="{Binding RelativeSource={RelativeSource Mode=FindAncestor, AncestorType={x:Type TabControl}}, Path=Items.Count}" Value="1">
                        <Setter Property="Visibility" Value="Collapsed"/>
                    </DataTrigger>
                </Style.Triggers>                
            </Style>
        </TabControl.ItemContainerStyle>
    </TabControl>
</Grid>

If you want to get rid of the TabControl completely if there is only one item, that logic should probably be at a higher level.

Here ist what I would do

public partial class MainWindow : Window
{
    public MainWindow()
    {
        InitializeComponent();
    }

    private void Window_Loaded(object sender, RoutedEventArgs e)
    {
        //create all 
        var customers = new List<Customer>{
            new Customer {FirstName = "Jim", LastName = "Smith", NumberOfContracts = 23},
            new Customer {FirstName = "Jane", LastName = "Smith", NumberOfContracts = 23},
            new Customer {FirstName = "John", LastName = "Tester", NumberOfContracts = 23}};

        //show 
        TheTabControl.ItemsSource = customers;
        TheTabControl.SelectedIndex = 0;
    }


public class Customer
{
    public string FirstName { get; set; }
    public string LastName { get; set; }
    public int NumberOfContracts { get; set; }
}

And on the XAML side

<TabControl x:Name="TheTabControl">            
    <TabControl.ItemTemplate>
        <DataTemplate>                    
            <TextBlock>                            
                <TextBlock Text="{Binding FirstName}"/> <TextBlock Text="{Binding LastName}"/>
            </TextBlock>                        
        </DataTemplate>
    </TabControl.ItemTemplate>
    <TabControl.ContentTemplate>
        <DataTemplate>
            <TextBlock>                            
                This is <TextBlock Text="{Binding FirstName}"/> <TextBlock Text="{Binding LastName}"/>
            </TextBlock>
        </DataTemplate>
    </TabControl.ContentTemplate>
</TabControl>